TSTP Solution File: SYN059+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN059+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:26 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN059+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:41:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(big_j_type, type, (
% 0.20/0.38 big_j: $i > $o)).
% 0.20/0.38 tff(tptp_fun_U_3_type, type, (
% 0.20/0.38 tptp_fun_U_3: $i)).
% 0.20/0.38 tff(big_h_type, type, (
% 0.20/0.38 big_h: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: $i)).
% 0.20/0.38 tff(big_g_type, type, (
% 0.20/0.38 big_g: $i > $o)).
% 0.20/0.38 tff(big_f_type, type, (
% 0.20/0.38 big_f: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_2_type, type, (
% 0.20/0.38 tptp_fun_X_2: $i)).
% 0.20/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.38 tptp_fun_Y_1: $i)).
% 0.20/0.38 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.38 tptp_fun_Y_4: $i)).
% 0.20/0.38 tff(tptp_fun_W_5_type, type, (
% 0.20/0.38 tptp_fun_W_5: $i)).
% 0.20/0.38 tff(1,assumption,(~(big_h(X!2) | (~big_f(X!2)))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((big_h(X!2) | (~big_f(X!2))) | (~big_h(X!2))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (~big_h(X!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (((~big_h(X!2)) | (~big_j(Y!1))) | big_h(X!2)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~big_h(X!2)) | (~big_j(Y!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 ((big_h(X!2) | (~big_f(X!2))) | big_f(X!2)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (big_f(X!2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.20/0.38 tff(8,assumption,(~((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U)))))), introduced(assumption)).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U))))) | ![U: $i] : (big_j(U) | (~big_g(U)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![U: $i] : (big_j(U) | (~big_g(U)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U))))) | ![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.20/0.38 tff(13,assumption,(~((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))), introduced(assumption)).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) | ((~big_h(W!5)) | (~big_j(Y!4)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~big_h(W!5)) | (~big_j(Y!4))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) | big_g(Y!4)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (big_g(Y!4)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[16, 13])).
% 0.20/0.38 tff(18,assumption,(![U: $i] : (big_j(U) | (~big_g(U)))), introduced(assumption)).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (((~![U: $i] : (big_j(U) | (~big_g(U)))) | (big_j(Y!4) | (~big_g(Y!4)))) <=> ((~![U: $i] : (big_j(U) | (~big_g(U)))) | big_j(Y!4) | (~big_g(Y!4)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~![U: $i] : (big_j(U) | (~big_g(U)))) | (big_j(Y!4) | (~big_g(Y!4)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~![U: $i] : (big_j(U) | (~big_g(U)))) | big_j(Y!4) | (~big_g(Y!4))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (big_j(Y!4)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[21, 18, 17])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) | big_f(W!5)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (big_f(W!5)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[23, 13])).
% 0.20/0.38 tff(25,assumption,(![X: $i] : (big_h(X) | (~big_f(X)))), introduced(assumption)).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(W!5) | (~big_f(W!5)))) <=> ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(W!5) | (~big_f(W!5)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(W!5) | (~big_f(W!5)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(W!5) | (~big_f(W!5))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (big_h(W!5)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[28, 25, 24])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~((~big_h(W!5)) | (~big_j(Y!4)))) | (~big_h(W!5)) | (~big_j(Y!4))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 29, 22, 15])).
% 0.20/0.39 tff(32,plain,(((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) | (~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 12, 10])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(X!2) | (~big_f(X!2)))) <=> ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(X!2) | (~big_f(X!2)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(X!2) | (~big_f(X!2)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(X!2) | (~big_f(X!2))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[36, 25, 3, 7])).
% 0.20/0.39 tff(38,plain,((big_h(X!2) | (~big_f(X!2))) | (~![X: $i] : (big_h(X) | (~big_f(X))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (big_h(X!2) | (~big_f(X!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[38, 12])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4))))) <=> ((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ((((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) | ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) & (((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3))))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4)))))) <=> (((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) | ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) & ((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) <=> ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))) <=> ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (((![X: $i] : (big_f(X) => big_h(X)) & ![U: $i] : (big_g(U) => big_j(U))) <=> ![W: $i, Y: $i] : ((big_f(W) & big_g(Y)) => (big_h(W) & big_j(Y)))) <=> ((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~((![X: $i] : (big_f(X) => big_h(X)) & ![U: $i] : (big_g(U) => big_j(U))) <=> ![W: $i, Y: $i] : ((big_f(W) & big_g(Y)) => (big_h(W) & big_j(Y))))) <=> (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~((![X: $i] : (big_f(X) => big_h(X)) & ![U: $i] : (big_g(U) => big_j(U))) <=> ![W: $i, Y: $i] : ((big_f(W) & big_g(Y)) => (big_h(W) & big_j(Y))))) <=> ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.39 tff(47,axiom,(~((![X: $i] : (big_f(X) => big_h(X)) & ![U: $i] : (big_g(U) => big_j(U))) <=> ![W: $i, Y: $i] : ((big_f(W) & big_g(Y)) => (big_h(W) & big_j(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel29')).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 42])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((~(![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U))))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[53, 42])).
% 0.20/0.39 tff(55,plain,(
% 0.20/0.39 ((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) | ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) & (((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3))))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[54])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) | ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) & ((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 41])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4))))),
% 0.20/0.39 inference(and_elim,[status(thm)],[56])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 ((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[57, 40])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (~(big_j(U!3) | (~big_g(U!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[58, 39, 33])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((big_j(U!3) | (~big_g(U!3))) | big_g(U!3)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (big_g(U!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((big_j(U!3) | (~big_g(U!3))) | (~big_j(U!3))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (~big_j(U!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (((~![U: $i] : (big_j(U) | (~big_g(U)))) | (big_j(U!3) | (~big_g(U!3)))) <=> ((~![U: $i] : (big_j(U) | (~big_g(U)))) | big_j(U!3) | (~big_g(U!3)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~![U: $i] : (big_j(U) | (~big_g(U)))) | (big_j(U!3) | (~big_g(U!3)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((~![U: $i] : (big_j(U) | (~big_g(U)))) | big_j(U!3) | (~big_g(U!3))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[66, 10, 63, 61])).
% 0.20/0.39 tff(68,plain,((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (((~((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U)))))) | ![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) <=> ((~((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U)))))) | ![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) | ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) <=> ((~((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U)))))) | ![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 ((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) | ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[56])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 ((~((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U)))))) | ![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 ((~((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U)))))) | ![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[73, 68])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (?[Y: $i] : big_g(Y) <=> ?[Y: $i] : big_g(Y)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(76,axiom,(?[Y: $i] : big_g(Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel29_2')).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (?[Y: $i] : big_g(Y)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.39 tff(78,plain,(
% 0.20/0.39 big_g(Y!1)),
% 0.20/0.39 inference(skolemize,[status(sab)],[77])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_f(X!2)) | (~big_g(Y!1)) | (~((~big_h(X!2)) | (~big_j(Y!1)))))) <=> ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | (~big_f(X!2)) | (~big_g(Y!1)) | (~((~big_h(X!2)) | (~big_j(Y!1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (((~big_g(Y!1)) | (~big_f(X!2)) | (~((~big_h(X!2)) | (~big_j(Y!1))))) <=> ((~big_f(X!2)) | (~big_g(Y!1)) | (~((~big_h(X!2)) | (~big_j(Y!1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_g(Y!1)) | (~big_f(X!2)) | (~((~big_h(X!2)) | (~big_j(Y!1)))))) <=> ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_f(X!2)) | (~big_g(Y!1)) | (~((~big_h(X!2)) | (~big_j(Y!1))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_g(Y!1)) | (~big_f(X!2)) | (~((~big_h(X!2)) | (~big_j(Y!1)))))) <=> ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | (~big_f(X!2)) | (~big_g(Y!1)) | (~((~big_h(X!2)) | (~big_j(Y!1)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_g(Y!1)) | (~big_f(X!2)) | (~((~big_h(X!2)) | (~big_j(Y!1)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | (~big_f(X!2)) | (~big_g(Y!1)) | (~((~big_h(X!2)) | (~big_j(Y!1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[84, 78, 74, 7, 5])).
% 0.20/0.40 tff(86,plain,(big_h(X!2) | (~big_f(X!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))) <=> ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | (~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (((~big_g(Y!4)) | (~big_f(W!5)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) <=> ((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_g(Y!4)) | (~big_f(W!5)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))) <=> ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_g(Y!4)) | (~big_f(W!5)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))) <=> ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | (~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_g(Y!4)) | (~big_f(W!5)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | (~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[92, 74, 24, 17, 15])).
% 0.20/0.40 tff(94,plain,((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (~(big_j(U!3) | (~big_g(U!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[58, 94, 86])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 (~big_j(U!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[62, 95])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (((~big_h(X!0)) | (~big_j(U!3))) | big_j(U!3)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 ((~big_h(X!0)) | (~big_j(U!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 (big_g(U!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[60, 95])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 (?[X: $i] : big_f(X) <=> ?[X: $i] : big_f(X)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(101,axiom,(?[X: $i] : big_f(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel29_1')).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (?[X: $i] : big_f(X)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.40 tff(103,plain,(
% 0.20/0.40 big_f(X!0)),
% 0.20/0.40 inference(skolemize,[status(sab)],[102])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 (((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_g(U!3)) | (~big_f(X!0)) | (~((~big_h(X!0)) | (~big_j(U!3)))))) <=> ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | (~big_g(U!3)) | (~big_f(X!0)) | (~((~big_h(X!0)) | (~big_j(U!3)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | ((~big_g(U!3)) | (~big_f(X!0)) | (~((~big_h(X!0)) | (~big_j(U!3)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 ((~![W: $i, Y: $i] : ((~big_g(Y)) | (~big_f(W)) | (~((~big_h(W)) | (~big_j(Y)))))) | (~big_g(U!3)) | (~big_f(X!0)) | (~((~big_h(X!0)) | (~big_j(U!3))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[106, 103, 74, 99, 98])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------